It's like you said about yourself, you want fun and relax, then to me that's a casual gamer, basically like watching TV but playing a game. Nothing wrong with that at all. When I feel that way rarely, I'll throw in some Witcher 3 at times. But mostly for me it's serious gaming or not game at all. If I don't want to play serious then I most likely just watch some shows or surf the web rather than playing something more laid-back. It's just my personality.
From what you're saying, your definition is plain wrong and should be updated.
You can be a hardcore book reader, what do you do? Read books.
Hardcore TV series fan, what do you do? Watch TV series.
If you're a hardcore bicycle rider, you probably ride bicycle a lot.
And then there is an elitist hardcore gamer, who has to compete online (in a super narrow amount of games, since you know, most games are offline and then amongst those online are elite - selected for today's e-sport). It's straight bullshit. Your hardcore gamer term is nothing other than either amateur or pro e-sport player. Think of all those who were there when it all started, how can you take that away from people who never got into online, but spent thousands of hours in single player games?
I won first league in FIFA 18 couple of times, since it's only game I used to play online for a while, but you think I might be a casual, just because I prefer to know what happened with Ethan Carther?
Hell, I graduated as video game developer, I guess that pretty much tells how different gamer I am from girls playing Sims and folks playing FIFA once in a while.
Not playing online is nowhere close to "not playing serious". I'm dead serious saving Ciri. I'm just not serious killing folks over and over again in CoD, because it's repetitive.
The best term from urban dictionary:
"Hardcore gamers put good gameplay above all else, and don't mind if a good game has poor (or even nonexistent) graphics, sound, characters and plot. "
This is probably the best you'll get in terms of a true hardcore gamer. It's just a game lover, not some kind of elitist guy who mastered couple of online games. Quite opposite to world of online games, the entire gaming world is a big one. Too big for any of e-sport players to steal the "hardcore gamer" term. You don't need to know Fortnite characters, but you do need to know Blazkowicz.
@eochaid - I also get piracy, but Assassin's Creed is a good product - especially part 2 + Brotherhood + Revelations, fantastic trilogy. Also IV and Origins were really nice. Most of the unfinished product are online related, as is Anthem, The Division, Destiny, which are good to play after a year or so. Ubisoft is a fine company who gave us really good games and I don't understand all the hate towards them. They sometimes made terribly bad decisions about their anti-theft policy, but some of the franchises we had from them are fantastic, i.e. Far Cry, Splinter Cell, Beyond Good & Evil. Much better than EA and Activision.